A new analytic ram pressure profile for satellite galaxies
Cristian A. Vega-Martínez, Facundo A. Gómez, Sofía A. Cora, Tomás Hough
aa r X i v : . [ a s t r o - ph . GA ] J a n MNRAS , 1–13 (2021) Preprint 2 February 2021 Compiled using MNRAS L A TEX style file v3.0
A new analytic ram pressure profile for satellite galaxies
Cristian A. Vega-Martínez, , ★ Facundo A. Gómez, , Sofía A. Cora, , Tomás Hough , Instituto de Investigación Multidisciplinar en Ciencia y Tecnología, Universidad de La Serena, Raúl Bitrán 1305, La Serena, Chile Departamento de Astronomía, Universidad de La Serena, Av. Juan Cisternas 1200 Norte, La Serena, Chile Instituto de Astrofísica de La Plata (CCT La Plata, CONICET, UNLP), Paseo del Bosque s/n, La Plata, Argentina Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo del Bosque s/n, La Plata, Argentina
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We analyse two analytic fitting profiles to model the ram pressure exerted over satellites galax-ies for different environments and epochs, using hydrodynamical resimulations of groups andclusters of galaxies to measure the ram pressure from the gas particle distribution. First, wecompare the predictions given by a known 𝛽 –profile model with the simulation measurements,finding that the profile is not in agreement with the expected behaviour by missing the depen-dence with the halo mass and halocentric distance. It features a systematic underestimationof the predicted ram pressure at high redshifts ( 𝑧 > . 𝑟 < . 𝑅 vir . This behaviour reverses as redshift decreases, featuring anincreasing over-estimation with halocentric distance at 𝑧 =
0. As an alternative, we introducea new universal analytic model for the profiles consisting in a damped power law, and weprovide a new set of fitted parameters which can recover the ram pressure dependence onhalo mass and redshifts. Finally, we analyse the impact of these analytic profiles in the galaxyproperties by applying a semi-analytic model of galaxy formation and evolution on top of thesimulations. We find the number of galaxies experiencing large amounts of accumulated rampressure stripping have low stellar mass ( 𝑀 ★ ≤ M ⊙ ), and their specific star formation ratesdepend significantly on the pressure modelling, particularly at high redshifts ( 𝑧 > . Key words: galaxies: general – galaxies: interactions – galaxies: evolution – galaxies: clusters:general – methods: numerical
During the last decades, observations of the galaxy popula-tion inhabiting different environments have shown a clear bi-modal distribution in several galaxy properties including colours,morphology, stellar ages and star formation rates, among oth-ers (e.g. Kauffmann et al. 2003; Baldry et al. 2004; Cassata et al.2008; Thomas et al. 2010; Peng et al. 2010; Wetzel et al. 2012;Taylor et al. 2015). This suggests a division between galaxies dom-inated by recently formed stellar populations and galaxies with oldstellar content. A critical difference between these populations isthe depletion of the global star formation activity. This state, alsoreferred to as galaxy quenching, is generally defined when the spe-cific star formation rate (sSFR) of a galaxy, i.e. the rate of starsformed divided by its stellar mass, decreases below a certain value,usually 10 − yr − (Weinmann et al. 2010; De Lucia et al. 2012;Wetzel et al. 2013).The contribution to the star formation quenching from the dif-ferent physical processes driving galaxy evolution is still a topic ★ E-mail: [email protected] of debate (see Somerville & Davé 2015, for a review on phys-ical models on galaxy formation). Two different types of pro-cesses have been invoked in the suppression of the star forma-tion: mass- and environmental- quenching (Peng et al. 2010). Thischaracterisation of the quenching processes gave rise to the known nature versus nurture discussion to disentangle the main driversof the evolution of galaxy properties. Comparisons between theproperties of populations of star-forming (active) and quiescent(passive) galaxies have shown that, up to 𝑧 ∼
1, it is possibleto identify the main mechanism driving them to the quenchingstate (e.g. Baldry et al. 2006; Peng et al. 2010; Muzzin et al. 2012;Kovač et al. 2014; Guglielmo et al. 2015; van der Burg et al. 2018,2020). This, however, does not necessarily mean that they are phys-ically unrelated. At higher redshifts, the picture is more intriguing.The median star formation rate (SFR) of galaxies and the quenchedfraction (i.e. the ratio between the number of quenched galaxiesand the total number of galaxies, including quenched and star-forming ones) are observed to be independent of the environment(e.g. Darvish et al. 2016). However, it has also been argued thatthe environment can have an impact on galaxy quenching even © C.A. Vega-Martínez et al. up to 𝑧 ∼ . 𝑧 & 𝑀 ★ . M ⊙ ) ratherthan for higher mass ones (Haines et al. 2006; Bamford et al. 2009;Peng et al. 2010; Roberts et al. 2019), and this has been supportedby theoretical analysis (e.g. De Lucia et al. 2012; Cora et al. 2018;Xie et al. 2020). Besides, environmental quenching is more evi-dent when analysing the largest over-densities, where galaxy clus-ters are located ( 𝑀 halo ≈ M ⊙ ). Analysis of dense regions inthe local Universe have shown higher fractions of quenched galax-ies (e.g. van den Bosch et al. 2008; Gavazzi et al. 2010), being thesSFR of the satellite galaxies significantly smaller in clusters than inlower density regions (e.g. Haines et al. 2013), and this behaviour isalso present in high redshift clusters (e.g. van der Burg et al. 2018,2020).The suppression of the gas accretion into the galaxy disc(usually referred to as starvation , Larson et al. 1980) and the lossof gas from galaxy disc due to the interaction with the mediumthrough ram pressure stripping (RPS, Gunn & Gott 1972) have beenthe two processes most commonly associated to the quenching ofsatellite galaxies in galaxy clusters (Quilis et al. 2000; Wetzel et al.2013; Muzzin et al. 2014; Peng et al. 2015; Jaffé et al. 2015), andalso in the Local Group (e.g. Fillingham et al. 2015; Wetzel et al.2015). A critical difference between the effect of each processis the quenching timescale inferred from the galaxy properties.For starvation, once the feeding of gas to the satellite halts, thestar formation of the galaxy can be suppressed in & . 𝑀 ★ . M ⊙ ) is mainly driven byram pressure, whereas starvation dominates quenching of galaxieswith 𝑀 ★ & M ⊙ (Fillingham et al. 2015; Wetzel et al. 2015).Nonetheless, recent observations indicate that environment mayhave a negligible role in the quenching of ultra faint galaxies ob-served in the Local Group (Rodriguez Wimberly et al. 2019). The differentiation between these processes becomes more complicatedwhen we consider that ram pressure can also strip part of the hot halogas of the galaxy, without necessarily acting over the disc, leadingto a starvation scenario (Bekki et al. 2002; Steinhauser et al. 2016).Moreover, there are theoretical analysis indicating that this strip-ping process is an important ingredient to consistently predict thequenched fraction of satellites on different environments (Cora et al.2018, 2019; Xie et al. 2020). In general, there is increasing observa-tional evidence connecting the lack of circumgalactic medium andgalaxy quenching (e.g. Kacprzak et al. 2020).Due to the hierarchical growing of the dark matter halos(White & Rees 1978; Davis et al. 1985), a large fraction of the satel-lites of 𝑧 = pre-processing stage be-fore falling into larger systems (e.g De Lucia et al. 2012; Jaffé et al.2015; Pallero et al. 2019, 2020). Moreover, recent analysis haveshown a strong dependence of the quenching fraction with theintra-cluster medium (ICM) density, featuring a specific thresh-old that determines a sharp increase in the quenching efficiency(Roberts et al. 2019; Pallero et al. 2020), raising the connection be-tween the different environments and the ram pressure exerted overthe satellites residing in them, favouring the importance of RPS as acrucial mechanism to understand the general galaxy quenching pro-cess. Thereby, this work is focused in the ram pressure modellingusing analytical approaches obtained from numerical simulations.The next subsection describes the usual modelling of RPS appliedin different theoretical contexts. The ram pressure (RP) is the result of the interaction between thegalaxies and the medium surrounding them, across which they aremoving. In case of satellite galaxies, the RP is exerted by the ICMand is determined by the density of the medium in the satelliteposition and its orbital evolution. Specifically, it is defined by 𝑃 ram ≡ 𝜌 ICM 𝑣 , (1)where 𝜌 ICM is the ICM density in the host halo and 𝑣 is the relativevelocity between the satellite and the medium. Both quantities de-pend on the galactocentric distance of the satellite. Therefore, thisstrong dependence on satellite galactocentric distance must be ac-counted for when estimating the amount of stripped gas mass fromthe galaxy. When the restoring force of the galaxy is smaller than theRP, then the diffuse inter-stellar medium can be stripped from thesatellite (Gunn & Gott 1972; Abadi et al. 1999; Quilis et al. 2000;Vollmer et al. 2001; Jaffé et al. 2015). Furthermore, simulations ofgalaxies falling into large galaxy clusters have shown that a sin-gle transit of a galaxy through the ICM’s core can fully deplete itsatomic gas (e.g. Roediger & Brüggen 2007).According to this definition, the estimation of the effectiveRP exerted over a particular observed galaxy requires to define amodel of the host halo gas density profile, and to estimate the or-bital galaxy speed relative to the host (e.g. Rasmussen et al. 2008;Jaffé et al. 2015, 2018; Roberts et al. 2019). When analysing nu-merical simulations, on the other hand, the estimation depends onthe type of calculation considered. For example, dark matter–only 𝑁 –body cosmological simulations are unable to predict a consis-tent gas profile, as the baryonic components are not included in thecalculation. Nonetheless, a recently proposed Local BackgroundEnvironment (LBE) technique for estimating the influence of en-vironmental effects on galaxy evolution allows to approximate RP MNRAS , 1–13 (2021) new analytic ram pressure profile (Ayromlou et al. 2019), although it requires a detailed analysis ofthe particle distribution of the simulation.The most precise modelling scenario comes from hydrody-namic simulations. The properties of the gas particles included inthe calculation allow to directly measure the density of the ICMat the precise locations where the galaxies (i.e. subhalos) are lo-cated (Tecce et al. 2010). Thereby, these calculations allow to studythe evolution of the RP across cosmic time, to measure its depen-dence with host halo mass, and to even define analytic profiles tomodel it, as done by Tecce et al. (2011) (hereafter T11). Besides,these analytic profiles can be considered to consistently model thefraction of satellites’ mass stripped by RP over their evolution withsemi-analytic models (SAM) of galaxy formation (e.g. Cora et al.2018). SAMs are based on a set of analytic prescription to accountfor the main physical process driving galaxy formation and thuscan not self–consistently follow the gas distribution of galaxies.Such models are usually coupled to dark matter halo propertiesand merger trees obtained from cosmological simulations, or cre-ated from a Press-Schechter formalism (Press & Schechter 1974;Bond et al. 1991; Lacey & Cole 1993).As we have already mentioned, there is increasing evidenceindicating that RPS is a key process in galaxy evolution. Hence adetailed, accurate and simple modelling of this environmental effectis becoming highly demanded. Accordingly, the main topic of thiswork is the definition of RP analytic profiles as measured from cos-mological hydrodynamic simulations. In particular, we revisit thepredictions of the analytic profile presented by T11. We show thatit features important systematic differences between its predictionsfor the RP and the expected values measured in the simulationsconsidered in its original calculation. Moreover, we go further in-troducing a new analytic profile able to overcome those differencesin the predictions, achieving higher accuracy in the modelling. Thispaper is organised as follows. In Section 2, we describe the origi-nal T11 profile, detailing the simulations used in its estimation andwe analyse the problems found in its predictions. In Section 3, weintroduce the new analytic profile based on the same simulationsand show the improvements regarding the predictions. In Section 4,we evaluate the impact of the usage of these profiles in the galaxyproperties by the application of a SAM. Finally, in Section 5, wesummarise our analysis highlighting the main results. In T11, a set of N-body/Smooth Particle Hydrodynamic (SPH)adiabatic resimulations of clusters of galaxies were used to measurethe RP exerted on galaxies and thus to estimate RP profiles as afunction on the halocentric distances, redshifts and the main hosthalos virial masses. The resulting shapes of the RP profiles withinthese halos were characterised with a 𝛽 –profile (Tecce et al. 2010)and a numerical fit of its parameters were provided as a main result.In the following, we describe the simulations used in this work(also considered by T11) and present an overview and a subsequentanalysis of the T11 profile. As in T11, we use the N-body/SPH resimulations of clusters ofgalaxies described in Dolag et al. (2005, 2009). These correspondto resimulations of selected regions from a ∼
685 Mpc side-lengthvolume, characterised by a Λ CDM cosmology with Ω m = . Ω Λ = .
7, a Hubble constant 𝐻 =
70 km s − Mpc − and a power spectrum with normalization 𝜎 = .
9. The resimulations considera universal baryonic density Ω b = . . × ℎ − M ⊙ and gas particle mass 1 . × ℎ − M ⊙ (for more details about these simulations we refer the reader toDolag et al. 2009). The identification of the dark matter halos andthe construction of their corresponding merger trees were doneusing Subfind (Springel et al. 2001). The centre of each dark matterhalo was defined according to the position of its most bound darkmatter particle following the method implemented in the
Subfind algorithm. Properties like the virial mass and radius of the main hosthalos were obtained from the resulting density profiles given by thedistribution of the dark matter particles at each redshift. Assuming aspherical-overdensity criteria (Press & Schechter 1974), we definethe virial mass 𝑀 of each main host halo as the mass contained ina sphere of radius 𝑅 at which the density equate a Δ factor of thecritical density of the Universe. With a constant value of Δ = 𝑀 ( < 𝑅 ) = 𝜌 c 𝜋 𝑅 , (2)where 𝜌 c is the critical density of the Universe. As described inSpringel et al. (2001), each system of halos is characterised by thedetection of a main host halo (i.e. the largest overdensity foundover the background), for which general properties such as 𝑀 and 𝑅 are calculated. Then, Subfind identifies all the subhaloswithin each main host. Excluding the main subhalo correspondingto the host of the central galaxy of each system, all the other resolvedsubhalos are considered as satellite galaxies of the main host.The resimulations considered here are three regions centredin large overdensities corresponding to massive galaxy clusterswith 𝑀 ∼ ℎ − M ⊙ (originally labelled g1, g8 and g51in Dolag et al. 2005, 2009), and five regions corresponding to low-mass galaxy clusters with 𝑀 ∼ ℎ − M ⊙ (labelled g676,g914, g1542, g3344 and g6212). Excluding the systems contami-nated with massive boundary particles, each region also includes aset of resolved smaller clusters and groups, also considered in ouranalysis. The analytic RP profile introduced by T11 was obtained from thesimulations described above, using the positions and velocities ofthe satellites to trace the RP experienced by them at different galac-tocentric distances, epochs, and ranges of main host halo masses.Additionally they included the SAM of galaxy formation and evolu-tion, sag (Cora 2006; Lagos et al. 2008; Tecce et al. 2010), only toextend the sample of RP profile tracing points by incorporating theorphan satellite galaxies, which are followed by the semi-analyticmodelling. These orphans are galaxies that have been hosted byhalos which are no longer detected by the halo finder because theyhave either merged with the main host halo or their masses de-creased below the resolution limit of the simulation. Therefore, thepositions and velocities of these satellites are defined according tothe properties of the most bound particle of the halo to which eachgalaxy last belonged (see Tecce et al. 2010).As was shown in T11, the efficiency of RP increases with themass of the main host halo and with decreasing redshift. The best fit-ting profile was found to be a full 𝛽 –profile, commonly used for char-acterising the ICM around massive galaxies (e.g. Churazov et al. MNRAS000
Subfind algorithm. Properties like the virial mass and radius of the main hosthalos were obtained from the resulting density profiles given by thedistribution of the dark matter particles at each redshift. Assuming aspherical-overdensity criteria (Press & Schechter 1974), we definethe virial mass 𝑀 of each main host halo as the mass contained ina sphere of radius 𝑅 at which the density equate a Δ factor of thecritical density of the Universe. With a constant value of Δ = 𝑀 ( < 𝑅 ) = 𝜌 c 𝜋 𝑅 , (2)where 𝜌 c is the critical density of the Universe. As described inSpringel et al. (2001), each system of halos is characterised by thedetection of a main host halo (i.e. the largest overdensity foundover the background), for which general properties such as 𝑀 and 𝑅 are calculated. Then, Subfind identifies all the subhaloswithin each main host. Excluding the main subhalo correspondingto the host of the central galaxy of each system, all the other resolvedsubhalos are considered as satellite galaxies of the main host.The resimulations considered here are three regions centredin large overdensities corresponding to massive galaxy clusterswith 𝑀 ∼ ℎ − M ⊙ (originally labelled g1, g8 and g51in Dolag et al. 2005, 2009), and five regions corresponding to low-mass galaxy clusters with 𝑀 ∼ ℎ − M ⊙ (labelled g676,g914, g1542, g3344 and g6212). Excluding the systems contami-nated with massive boundary particles, each region also includes aset of resolved smaller clusters and groups, also considered in ouranalysis. The analytic RP profile introduced by T11 was obtained from thesimulations described above, using the positions and velocities ofthe satellites to trace the RP experienced by them at different galac-tocentric distances, epochs, and ranges of main host halo masses.Additionally they included the SAM of galaxy formation and evolu-tion, sag (Cora 2006; Lagos et al. 2008; Tecce et al. 2010), only toextend the sample of RP profile tracing points by incorporating theorphan satellite galaxies, which are followed by the semi-analyticmodelling. These orphans are galaxies that have been hosted byhalos which are no longer detected by the halo finder because theyhave either merged with the main host halo or their masses de-creased below the resolution limit of the simulation. Therefore, thepositions and velocities of these satellites are defined according tothe properties of the most bound particle of the halo to which eachgalaxy last belonged (see Tecce et al. 2010).As was shown in T11, the efficiency of RP increases with themass of the main host halo and with decreasing redshift. The best fit-ting profile was found to be a full 𝛽 –profile, commonly used for char-acterising the ICM around massive galaxies (e.g. Churazov et al. MNRAS000 , 1–13 (2021)
C.A. Vega-Martínez et al. 𝑃 ram ( 𝑀, 𝑧 ) = 𝑃 ( 𝑀, 𝑧 ) " + (cid:18) 𝑟𝑟 s ( 𝑀, 𝑧 ) (cid:19) − 𝛽 ( 𝑀,𝑧 ) , (3)where the central value 𝑃 , the characteristic radius 𝑟 s and theexponent 𝛽 are free parameters which depend on both the hosthalo mass and the redshift. In T11, these parameters were fitted fordifferent samples, covering a set of bins in main host halo masses,and for each simulation snapshot in the redshift range 0 ≤ 𝑧 ≤
3. Toobtain the dependence of these parameters on the redshift, a linearrelation in terms of the expansion factor of the Universe, 𝑎 , wasproposed according tolog (cid:18) 𝑃 − ℎ dyn cm − (cid:19) = 𝐴 𝑃 + 𝐵 𝑃 ( 𝑎 − . ) , (4) 𝑟 s 𝑅 = 𝐴 𝑟 + 𝐵 𝑟 ( 𝑎 − . ) , (5) 𝛽 = 𝐴 𝛽 + 𝐵 𝛽 ( 𝑎 − . ) , (6)where all the coefficients 𝐴 𝑖 and 𝐵 𝑖 with 𝑖 = 𝑃 , 𝑟 , or 𝛽 dependin principle on the main host virial mass. Additionally, a linearmodel following the expression 𝑎 + 𝑏 ( log 𝑀 − ) was proposedto parametrize the behaviour of each of the 𝐴 𝑖 and 𝐵 𝑖 coefficient,doubling in this way the total number of free parameters involved inthe fits. The numerical result of these twelve coefficients are givenby the equations (6a) to (6f) in T11. The resulting error associatedto each one of them was variable, reaching a maximum value of25% in a couple of cases. It was also found that both 𝐴 𝛽 and 𝐵 𝛽 were not dependent on the main host halo masses. Consequentlythe 𝛽 parameter was expressed only as a function on the redshift.Thereby, all the RP profiles in the analysed redshift range wereexpressed in terms of ten numerical constants which define theshape of the profiles according to time and host halo mass for eachsatellite galaxy inhabiting, at any radial distance, a main host darkmatter halo. Now we proceed to evaluate the reliability of the T11 RP profilemodel in predicting the effective RP exerted on satellite galaxies.To achieve this, we extract all the positions of the satellite halosbelonging to main host halos detected in the complete resimulatedregions described in Section 2.1, excluding only the main haloscontaminated with boundary particles. This considerably extend thenumber of inspected main host in comparison with T11, particularlyin the low-mass regime. Furthermore, this comparison is restrictedto only use the positions of the satellite halos identified by the halofinder, excluding all the extra tracers considered in T11 derived fromthe SAM (i.e. orphan satellites). Although this restriction reducesthe number of points to be used to define the profiles, it also limitsthe analysis only to the resimulations and their (sub)halos. We cantherefore avoid the usage of a SAM in this calculation.At each satellite position, we measure the effective RP obtainedfrom the simulation, 𝑃 simram , by following the method described inTecce et al. (2010). Here the ambient density and relative velocitywith respect to the satellite are measured using the gas particleslocated in a sphere centred at the position of the satellite, exclud-ing those associated to the subhalo. With these estimations, theequation (1) is directly applied. Besides, the predicted value of RPaccording to the T11 model, 𝑃 fitram , is also estimated at each satel-lite position. The comparison between these two values is shown in Fig. 1 for three different redshifts, 𝑧 =
0, 1 . 𝑟 / 𝑅 . As a reference, one standarddeviation around the mean is also included in the figure throughclosed rectangles for two selected radial distances in each case: at 𝑟 / 𝑅 = .
15 for the most massive host halos found at each red-shift, and at 𝑟 / 𝑅 = .
85 for the least massive ones. This allowsus to compare more precisely the host halo masses or redshifts atwhich the difference between the model and the measurements be-come more significant. As it can be appreciated from the figure,the T11 model overestimates the predicted RP at 𝑧 = ( 𝑀 [ ℎ − M ⊙ ]) >
15) where the 𝑃 fitram / 𝑃 simram ratio monotonically decreases towards the centre of thehosts. Here the profile underestimates the RP for satellites withindistances ≤ . 𝑅 . Moreover, the ratio exhibits a constant increasewith time, leading to a systematic underestimation of the predictedvalue of the RP with respect to the one measured at higher redshifts,( 𝑧 & .
5) for all the analysed halo mass ranges. These differencesbecome more important for the innermost satellites ( 𝑟 < . 𝑅 )of the most massive halos, where the underestimation is present atany redshift, reaching even two decades at 𝑧 ∼
3. This drawback ofthe T11 model is particularly troublesome if we consider that thesesatellites experience the highest values of RP during their evolu-tion. Thus, this underestimation can have an important impact inthe amount of gas stripped from the galaxies due to this environ-mental effect, changing the overall amount of gas available to formstars.The resulting inaccurate behaviour can be explained byanalysing the effect of the 𝑃 parameter on the prediction. Thisfactor regulates the zero point of the RP profile inside the hosts,thus modulating the maximum value of 𝑃 ram reachable towardstheir centres; a behaviour strongly dependent on the halo mass.Since the fit presented by T11 was constituted by several chi squareminimizations, starting with the evolution in terms of the expansionfactor of the Universe using linear models, the dependence with themass was inadvertently softened creating an artificial bias. This biascan even be noticed in the upper panel of the Fig. 4 in T11, in whichan example of the fit to the evolution of 𝑃 over the expansion factoris shown for a specific main halo mass range. Even though the over-lapped best linear fit follows the measured points and it is alwaysinside the estimated errors, this fit has a clear trend to underestimatethe value of 𝑃 as redshift decreases, reaching differences with re-spect to the original value greater than one decade. It is clear that,even in that first T11 fitting process, the original trend of the param-eter is lost and the prediction is softened due to the weight of themeasurements in all the considered redshift range. Therefore, the bi-ased behaviour of the T11 model was a result of the high number offree parameters used and the consecutive minimizations performedto complete the process. The possible degeneracies between the tenparameters and the high dispersion on the data preclude from find-ing a predictive model which can reproduce consistently the highestvalues of the RP inside massive main host halos. MNRAS , 1–13 (2021) new analytic ram pressure profile − − l og ( P fi t r a m / P s i m r a m ) z = . z = . z = . z = . z = . − − l og ( P fi t r a m / P s i m r a m ) z = . z = . z = . z = . z = . . . . . . . r / R − − l og ( P fi t r a m / P s i m r a m ) z = . z = . z = . z = . z = . ≤ log M < ≤ log M < ≤ log M < ≤ log M < ≤ log M Figure 1.
Ratio between the RP predicted by the T11 analytic model, 𝑃 fitram ,and the RP measured from the gas particles of the simulations, 𝑃 simram , in log-arithmic scale, for 𝑧 = , . and . in the upper , middle and bottom panels,respectively. The measurements are shown with respect to the galactocentricdistance normalised to 𝑅 , grouped according to the instantaneous mainhost halo mass and shown with different line styles and colours, as detailedin the legend. Empty squares show the size of the chosen bin in the relativedistance (horizontal) and one standard deviation around the mean (vertical),depicted at 𝑟 / 𝑅 = . ( . ) for the most (least) massive host halosample, respectively. With the aim of having a more accurate model for the RP profile, werecreated the original T11 fit, but also tried an alternative analyticversion by inverting the order in which redshift and halo mass de-pendencies are modelled for the 𝑃 , 𝑟 s and 𝛽 parameters. However,no improvements in the predictions were found with this exercise.Therefore, the profile as proposed by T11 does not constitute amodel consistent for different epochs and host halo masses.In order to find a model with better agreement, a different ap-proach must be taken. The described limitations forces us to providean analytical description of the RP profiles capable of reproducingtheir behaviour for different halo mass ranges at a given redshift,using the minimum number of free parameters. Moreover, due tothe need of expressing the temporal evolution of those parameters,degeneracies between them must be avoided.An example of the measured RP on the simulations, usingthe Tecce et al. (2010) technique, can be seen in Fig. 2. Here, thevalues of 𝑃 ram for the complete sample of satellites found at 𝑧 = − − − − − l og ( P r a m [ h dyn c m − ] ) ≤ log M ≤ log M < . . . r / R − − − − − l og ( P r a m [ h dyn c m − ] ) ≤ log M <
14 0 . . . r / R ≤ log M < Figure 2.
Complete set of RP values obtained by applying the Tecce et al.(2010) technique on each satellite of the selected halos from the resimulatedregions at 𝑧 = , as a function of halocentric distance normalized with thevirial radius of the halo, for different halo mass ranges. For reference, allpanels depict the complete set of measurements with light purple dots. Eachpanel highlights, with dark purple dots, the measurements corresponding tothe satellites from host halos selected according to the mass range indicatedin each legend. all the four panels of the figure. Each panel highlights, with darkpurple dots, the satellites that belong to a given mass range, asindicated on the key at the bottom.According to this, the proposed expression should be able tofollow the steep increment of the RP towards the centre of themassive host halos, which are the systems imprinting the RP inthe stronger regime and have a higher impact in their star–formingsatellites. The expression should also be able to reproduce simulta-neously the flatter behaviour observed at different radial distancesfor the less massive halos. This can be achieved with a simpledamped power law defined by 𝑃 ram ( 𝑀, 𝑧 ) = 𝑃 ( 𝑧 ) (cid:20) 𝜉 ( 𝑧 ) (cid:18) 𝑟𝑅 (cid:19)(cid:21) − 𝛼 ( 𝑀 ,𝑧 ) , (7)where 𝑟 / 𝑅 is the relative distance of the satellite to the centreof the host halo in terms of the virial radius, and 𝑃 ( 𝑧 ) , 𝜉 ( 𝑧 ) ,and 𝛼 ( 𝑀, 𝑧 ) are free parameters to define the shape of the profile.The 𝑃 ( 𝑧 ) parameter, expressed in units of ℎ dyn cm − , definesthe normalization of the profile, whereas the dimensionless 𝜉 ( 𝑧 ) determines the radial scaling, both dependent only on the redshift.The power 𝛼 ( 𝑀, 𝑧 ) encapsulates the dependence on the host halomass 𝑀 following a linear relation in logarithmic scale accordingto 𝛼 ( 𝑀 , 𝑧 ) = 𝛼 M ( 𝑧 ) log (cid:16) 𝑀 ℎ − [ M ⊙ ] (cid:17) + 𝛼 N , (8)where 𝛼 M ( 𝑧 ) and 𝛼 N are the free parameters to set the linear modelof the power. To break the evident degeneracy between these lasttwo parameters, a fixed value of 𝛼 N = − . MNRAS , 1–13 (2021)
C.A. Vega-Martínez et al. − − l og (cid:16) P − h dyn c m − (cid:17) log (cid:16) P − h dyn cm − (cid:17) = . a − . − . ξ ξ = − . a − . + . . . . . . a . . . α M α M = . × − a . + . Figure 3.
Temporal evolution, in terms of the scale factor 𝑎 , of the 𝑃 ( 𝑧 ) ( upper ), 𝜉 ( 𝑧 ) ( center ), and 𝛼 𝑀 ( 𝑧 ) ( bottom ) parameters of the introducedRP analytic profile. Blue dots show the numerical values found in the fittingprocess at each snapshot, with the errors bars extracted from the diagonalelements of the covariant matrices. Solid coloured lines show the fittedmodel of each parameter. The corresponding analytic expression is indicatedin each legend. minimums for the remaining three parameters is guaranteed in theminimisation processes.Thereby, by using the equations (7) and (8) as a new model forthe RP, we proceed to fit the three free parameters in each one ofthe resimulation snapshots through chi square minimizations. Thisis done simultaneously considering all the measurements of theRP at each redshift. Consequently, each minimization is performedconsidering all the available range in host halo mass covered by thecomplete set of resimulations. As described in the previous section,only the positions of the satellite halos are used in this procedure todefine the points to measure and fit the RP profile. Furthermore, herewe consider the whole redshift range covered by the halos of thesesimulations (0 ≤ 𝑧 < .
5) to perform the minimization, instead ofthe restricted range (0 ≤ 𝑧 ≤
3) adopted by T11.The low degeneracy between these three parameters can beseen in the smooth behaviour of the curves shown in Fig. 3. Here,the resulting numerical values obtained from all the fits of the pa-rameters that characterise the RP profile at each redshift are shownin blue dots, and each snapshot is shown in terms of the expansionfactor of the Universe 𝑎 . The reported errors, included as verticallines around each dot, are extracted directly from the diagonal ele-ments of the covariant matrices obtained from the fits, assuming nocorrelation between them. In the three cases, a very smooth tempo-ral evolution of the numerical values is found. This is exactly thetype of behaviour which allows to recover the desired predictabilityof the 𝑃 ram model in the extreme cases of the massive halos.Finally, we model the temporal evolution of these parametersthrough simple power laws with respect to the expansion factor,including a shift in the vertical axis, according to P = 𝜆 𝑎 𝜆 + 𝜆 , (9) Param. 𝜆 𝛿𝜆 𝜆 𝛿𝜆 𝜆 𝛿𝜆 log ( 𝑃 ) 𝜉 -3.4 1.4 -0.42 0.12 10.2 1.4 𝛼 M . × − . × − . × − Table 1.
Resulting numerical values of the 𝜆 coefficients which describe thetemporal evolution of the 𝑃 , 𝜉 y 𝛼 M parameters defining the RP profile. Theuncertainties were extracted directly from the obtained covariance matrices. where P corresponds to any of the log ( 𝑃 ) , 𝜉 and 𝛼 M parameters,and the 𝜆 𝑖 with 𝑖 = , , 𝜆 𝑖 coefficients are listed in Table 1, together with their respectiveerrors resulting from the chi square minimization processes.According to the resulting values of the non diagonal elementsof the covariance matrices obtained from the fits (not included in thetable for simplicity), we find a degeneracy between the 𝜆 and 𝜆 coefficients. This is consistent with the reported errors associated toeach coefficient, which are smaller than the observed amplitude ofthe little ripples exhibited by the curves. Nevertheless, since thesevalues are explicitly included in the definition of the model, and theyare not being fitted inside another relation, any degeneracy foundat this level does not modify the resulting predictions for the RPmodel, thus becoming irrelevant.As a proof of the better behaviour or this new model, we repli-cate the analysis described in the Section 2.3 but comparing thisnew fitted model with the measured RP profile from the resimula-tions. This comparison is shown in Fig. 4. As in Fig. 1, here weshow the dependence of the ratio between the predicted values ofRP given by the model and the measurements from the simula-tions, on galactocentric distance normalized to 𝑅 . It considersthe location of satellites from different main host halo mass rangesat the same three redshifts previously analysed. According to thefigure, the original reported bias was successfully avoided in thisnew model and its accuracy was substantially enhanced. Most ofthe artificial dependencies with the relative distance to the centreand host halo mass featured by the T11 are not present in our newprofile. A slightly underestimation of the RP towards the centre ofthe most massive main halos at high redshifts, and a general over-estimation towards the outskirts can be appreciated. However, thesetrends are statistically meaningless considering the natural spreadof the measured data in the sample of halos.Accordingly, this new fit is predictive enough to model the RPat higher redshifts, in contrast to the capabilities of the T11 fit, andit can be used in different scopes to track the amount of gas beinglost by satellite galaxies orbiting within their host halos. In the nextsection, we evaluate the impact of a consistent treatment of thisenvironmental effect on satellite galaxies by comparing the resultsobtained from applying the new model of RP profile and the T11fit. In order to analyse the specific effect of RP in galaxy properties,a galaxy formation and evolution model must be applied in thesesimulations, including the stripping by RP.
MNRAS , 1–13 (2021) new analytic ram pressure profile − − l og ( P fi t r a m / P s i m r a m ) z = . z = . z = . z = . z = . − − l og ( P fi t r a m / P s i m r a m ) z = . z = . z = . z = . z = . . . . . . . r / R − − l og ( P fi t r a m / P s i m r a m ) z = . z = . z = . z = . z = . ≤ log M < ≤ log M < ≤ log M < ≤ log M < ≤ log M Figure 4.
Comparison between the RP obtained with the new analytic modelintroduced in this work and the one measured from the gas particles of thesimulations, for 𝑧 =
0, 1 . . upper , middle and bottom panels,respectively. The symbols, binning and selection details are the same as inFig. 1. To create the galaxy populations from these simulations, we con-sider the updated version of the semi-analytic model of galaxyformation sag (Cora 2006; Lagos et al. 2008; Tecce et al. 2010;Orsi et al. 2014; Muñoz Arancibia et al. 2015; Gargiulo et al. 2015;Cora et al. 2018). It uses the halo catalogues and merger trees to fol-low the evolution of the galaxy properties, assigning one galaxy toeach detected subhalo and solving a set of analytic relations betweenthe galaxy components across cosmic time.Among the included physical processes, the model considersthe radiative cooling of the hot halo gas, star formation (quiescentand in starbursts), and a detailed treatment of the chemical enrich-ment considering the contribution from stellar winds and differenttypes of supernovae (Cora 2006). Thereby, feedback from these su-pernovae is also considered. It features an updated treatment of thisfeedback, whose calculation includes an explicit dependence on red-shift based on relations measured from full-physics hydrodynamicalsimulations (Cora et al. 2018). It also follows the growth of mas-sive black holes in the centre of galaxies, and their correspondingfeedback which suppresses gas cooling (Lagos et al. 2008). Star-bursts can be triggered by galaxy mergers and disc instabilities,contributing to the formation of galaxy bulges (Lagos et al. 2008;Muñoz Arancibia et al. 2015; Gargiulo et al. 2015). Environmentaleffects like tidal and RP stripping are also included in the model.It incorporates a detailed treatment for RPS considering the gasmass loss from both the discs and the hot gas halo, so that satellite galaxies are processed according to a gradual starvation schemeof their hot gas (Tecce et al. 2010; Cora et al. 2018). An additionalmodel to analytically follow the orbital evolution of orphan satellitegalaxies is also considered (Delfino et al., in preparation), as theirpositions within the host halos are relevant for a consistent calcu-lation of environmental effects in those galaxies. Additionally, thefree parameters included in the modelled relations are usually cali-brated to a set of observed relations of galaxy properties, by usingthe
Particle Swarm Optimisation technique (Ruiz et al. 2015).The gradual starvation scheme to remove the hot gas of satellitegalaxies after infall replaces the instantaneous removal usually ap-plied in SAMs. This is a key ingredient to analyse the overall effectof RP acting on satellites residing in different environments. Thegradual stripping of the hot gas is based on the Font et al. (2008)model, considering the estimations from McCarthy et al. (2008)and assuming a spherical distribution of the gas. At each timestep,the model calculates a satellite–centric radius 𝑟 sat beyond whichthe gas is stripped using a dynamic time–scale (calculated as inZentner et al. 2005), following the condition 𝑃 ram > 𝛼 RP 𝐺 𝑀 sat ( 𝑟 sat ) 𝜌 hot ( 𝑟 sat ) 𝑟 sat , (10)where 𝛼 RP is a geometrical constant, 𝑀 sat is the total satellite mass, 𝜌 hot is the hot gas density of the satellite and 𝑃 ram is the RP exertedover the satellite, measured directly using the gas particles of the thesimulation (Tecce et al. 2010) or estimated from an analytic profile(Tecce et al. 2011). A general value of 𝛼 RP = 𝑀 sat considers the contribution ofthe hot gas mass integrated until 𝑟 sat , using a spherical isothermaldensity profile.When the ratio between the hot gas halo mass and the baryonicmass of a satellite galaxy decreases below 0 .
1, RP can strip massfrom the galaxy disc following the model of Tecce et al. (2010).The stripping radius is calculated by using the Gunn & Gott (1972)condition 𝑃 ram > 𝜋𝐺 Σ stars ( 𝑟 ) Σ cold ( 𝑟 ) , (11)where Σ stars and Σ cold are the surface densities of the stellar andgas components of the galaxy disc, respectively. Both are modelledwith exponential profiles with the same scale-length, initially cal-culated from the spin and radius of the dark matter subhalo hostingthe satellite galaxy. We refer the reader to Cora et al. (2018, 2019);Collacchioni et al. (2018) (and references therein) for more detaileddescriptions of all the physical processes implemented in sag , in-cluding the environmental effects considered here. We applied the galaxy formation model sag to the complete set ofresimulations of clusters of galaxies described in Sec. 2.1 to trace theevolution of the corresponding galaxy population. We consider thedark matter halos and their corresponding merger trees as initial andboundary conditions to follow the evolution of galaxy properties.The calculation of the baryonic content of the subhalos for tracinggalaxy components must consider the fraction of mass contained inthe gas particles. Hence subhalo masses are corrected accordingly.Therefore, we only use the gas particle distribution to measure thelocal RP acting over the semi-analytic satellite galaxies associatedto the corresponding dark matter halos, by applying the Tecce et al.(2010) technique.We create a fiducial galaxy population applying the full-physics sag model described in Cora et al. (2018). It considers the values of
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MNRAS000 , 1–13 (2021)
C.A. Vega-Martínez et al. the free parameters that were calibrated to a dark matter only simula-tion of 1 Gpc / ℎ of sidelength ( sag 𝛽 . variant detailed in Cora et al.2018, 2019) instead of tuning a new set of parameter values for thisnew resolution limit and cosmology. The calculation of RPS consid-ers the values of RP measured from the gas particle distribution ofthe simulation, 𝑃 simram . Besides, to isolate the effect of RPS, we dis-able the mass loss of gas and stars due to tidal stripping processes.To validate this model variant, we inspect the conditional luminos-ity function (CLF) of satellites. The resulting distributions featurea decreasing behaviour with an excess towards the fainter-end ofthe function, when using the Cora et al. (2018) parameter values incomparison with the results from Lan et al. (2016). Therefore, weincrease the parameters related with the efficiencies of supernovaefeedback to improve the CLFs shape. Although the break and slopesof the CLFs are recovered with this change, the simultaneous fit-ting of the normalization for all the main host mass ranges requiresa complete exploration of the set of model parameters. Hence, aswe aim to compare galaxies in specific main host mass ranges, wenotice this caveat and proceed with a fair model-to-model compar-ison restricted to each main host mass range. Besides, a completerecalibration of the current model, specifically focused on this setof resimulations, constitutes a computationally demanding task thatis outside the scope of this work.Subsequently, we create two additional variants of the galaxymodelling by considering different analytic estimations of RP: thefit of the RP profiles introduced by Tecce et al. (2011); and therevisited fit presented in this work, described and analysed in theprevious section.As the three galaxy models are identical except for the RPcalculation, the resulting number of satellite galaxies obtained foreach run are equal due to the semi-analytic processing workflow: themodel traces the evolution of the orphan galaxies and it decides theirmerger times before the properties of the stellar and gas content ofthe galaxies are calculated. Therefore, a direct comparison betweenthe satellite populations of the same clusters can be done. Besides,it is worth noting that when comparing conditional luminosity andmass functions of satellite galaxies within main hosts in differentmass ranges, the resulting number counts show no significant dif-ferences between the three model variants analysed throughout thissection. To understand the general impact of the RP modelling, we createtwo samples of satellite galaxies according to the mass of the mainhost halo they belong to. A massive sample, containing satellitesof simulated clusters with log ( 𝑀 ℎ − [ M ⊙ ]) >
15. This samplecontains the three main host halos of the simulations g1, g8 and g51(see Section 2.1). Satellites of this sample are expected to experiencethe strongest RP values, especially near their cluster centres. Thesecond sample is composed of all the satellites that belong to hostshalos with 13 ≤ log ( 𝑀 ℎ − [ M ⊙ ]) <
14, selected from the fullset of resimulations. Considering only the non-contaminated halos,this less massive sample includes the satellites belonging to 34 mainhost halos.We proceed to analyse these two samples in each of the threemodel variants. For an overall measuring of the RP effect, we takeinto account all the progenitors of the galaxies belonging to each 𝑧 = 𝑀 totRPS ( > 𝑧 ) , as thesum of all the stripping measurements of the sample until any given l og ( M t o t R PS ( > z ) h − / N g r [ M ⊙ ] ) log ( M h − [ M ⊙ ]) > ( M h − [ M ⊙ ]) > ( M h − [ M ⊙ ]) >
15 SPHThis workT11 profile . . . . . . . z l og ( M t o t R PS ( > z ) h − / N g r [ M ⊙ ] ) ≤ log ( M h − [ M ⊙ ]) < ≤ log ( M h − [ M ⊙ ]) < ≤ log ( M h − [ M ⊙ ]) < Figure 5.
Mean accumulative function of the total RP stripped gas mass ofsatellite galaxies until a redshift 𝑧 . The three model variants are depictedwith different line styles and colours: the fiducial model in dotted dark bluelines, the model using the new RP profile in solid cyan lines, and the modelusing the T11 profile in dashed orange lines. Each function considers thecomplete population of satellites belonging to different ranges of main hosthalo: satellites from the 3 massive clusters ( top panel ) and from the selected34 less massive main hosts with 13 ≤ log ( 𝑀 ℎ − [ M ⊙ ]) <
14 ( bottompanel ). redshift, 𝑧 . To quantify the complete effect of this environmentalprocess, 𝑀 totRPS ( > 𝑧 ) includes the gas stripped from both the gasdisc and hot halo gas components of the satellites. We then obtainthe mean of the cumulative function of stripped mass by dividing bythe number of main halos selected in each sample, N gr . The resultingfunction is shown in Fig. 5. The top panel shows the results of thesatellite sample from the higher main host mass, whereas the bottompanel shows the results for the lower mass sample. Each panel showsthe three model variants: the dotted dark blue lines show our fiducialmodel considering the RP as measured from the SPH simulation,the solid cyan lines show the model using our new analytic RPprofile, and the dashed orange lines show the model using the T11fit. For both mass ranges, the total amount of gas mass strippedtends to reach the same value at 𝑧 =
0, independently of the RPmodel. The values are approximately equivalent to the 2.3 and 0.8per cent of the mean main host total mass for the high and low masssamples, respectively. Therefore, this global stripping process seemssightly more significant towards higher cluster masses; an expectedbehaviour as the RP acting on satellites near the centre of their hostsis able to reach larger values when the mass of the main host is high(e.g. Wetzel et al. 2012; Haines et al. 2015). Nonetheless, it shouldbe warned that the effective final RP stripped mass amount has adirect dependence on the general modelling of galaxy evolution, i.e.the physical processes considered in the semi-analytic model andthe corresponding calibration of its free parameters. Besides, as thenumber of satellites and total mass of each system increases overcosmic time, the amount of mass involved in newer stripping eventsbecomes more significant than the older ones in this figure. This also
MNRAS , 1–13 (2021) new analytic ram pressure profile contributes to the similar behaviour of the accumulated RP strippedmass exhibited by the three model variants. On the other hand, thesmall knee near 𝑧 ∼ To quantify the effective impact of the RP on individual galaxies, wedefine the instantaneous fraction of the total stripped mass, 𝑓 RPS ( 𝑧 ) ,as the ratio between the accumulated stripped mass of a satellite andits stellar mass, i.e. 𝑓 RPS ( 𝑧 ) ≡ 𝑀 RPS ( > 𝑧 ) 𝑀 ★ ( 𝑧 ) , (12)where 𝑀 RPS ( > 𝑧 ) is the accumulated stripped mass of a satelliteuntil a redshift 𝑧 , and 𝑀 ★ ( 𝑧 ) is its instantaneous stellar mass at red-shift 𝑧 . The 𝑓 RPS distributions exhibited by the complete sample ofsatellites belonging to the three most massive clusters are analysedby counting the number of galaxies having different values of thisquantity per cluster unit. To analyse the distributions at differentredshifts, we consider the progenitors of the selected 𝑧 = 𝑀 RPS ( > 𝑧 ) in all their satellites, accord-ingly. Hence, N gr = ( 𝑀 ★ [ M ⊙ ]) ≥
8. We thenidentify their halos and used them to select the the correspondinggalaxies in the remaining two models for a direct comparison. The resulting function is shown in the Fig. 6. We consider three distinctepochs, 𝑧 = .
0, 1 . . . 𝑧 = . 𝑓 RPS as redshift increases, indicating a persistentsmaller fraction of stripped mass in the complete satellite galaxypopulation. The analytic fit presented in this work features a notice-able improvement in the modelling of the number of galaxies withlarge fractions of stripped mass although, as previously discussed,is unable to fully recover the total number of galaxies with largerfractions.An interesting feature of the distributions shown in Fig. 6 isthe global increasing mean values of 𝑓 RPS over time, exhibitedby the three variants of the galaxy formation model. As redshiftdecreases, there is an increasing number of satellite galaxies whoseaccumulated total mass lost by RPS is larger than their instantaneousstellar mass (i.e. log ( 𝑓 RPS ( 𝑧 )) > 𝑓 RPS ( 𝑧 ) following the me-dian value obtained from the fiducial model is chosen to select thegalaxies. The same cut applied to the three model variants allows usto compare galaxies that are being affected with analogue strippingprocesses. Thereby, differences in the number counts of galaxiesallow measuring the overall effect of using the analytic models toestimate RP. Median values, indicating the half of the distributions,are preferred instead of a larger fraction only for visualisation pur-poses. This guarantees a number of galaxies large enough to becompared in all considered redshifts. It is worth noting that trendsand general conclusions reported in this section are not affectedwhen the cut applied in the fraction is increased (e.g. using thevalue defining the highest quartile of the distribution instead ofthe median). Therefore, the chosen limits in 𝑓 RPS ( 𝑧 ) to select thegalaxy samples are 4 .
78, 1 .
30 and 0 .
67 for redshifts 0 .
0, 1 . .
0, respectively.The comparison between the selected galaxies properties fromthe three model variants is shown in Fig. 7. The differential galaxynumber counts according to their stellar mass, specific star forma-tion rate and ( 𝑔 − 𝑟 ) rest-frame colour are shown in the left, middleand right columns, respectively. The comparison includes the three MNRAS000
0, respectively.The comparison between the selected galaxies properties fromthe three model variants is shown in Fig. 7. The differential galaxynumber counts according to their stellar mass, specific star forma-tion rate and ( 𝑔 − 𝑟 ) rest-frame colour are shown in the left, middleand right columns, respectively. The comparison includes the three MNRAS000 , 1–13 (2021) C.A. Vega-Martínez et al. d N g a l / d l og ( f R PS ) / N g r z = . d N g a l / d l og ( f R PS ) / N g r z = . − − ( f RPS ( > z )) d N g a l / d l og ( f R PS ) / N g r z = . SPHNew profileT11 profile
Figure 6.
Number counts of satellite galaxies having different values of theirinstantaneous fraction of total stripped mass, defined by equation (12). Eachpanel shows a different redshift: 𝑧 =
0, 1 . top , centre and bottom panels, respectively. Fiducial model resulting distributions are depicted withdotted dark blue lines and shaded areas, whereas the new and T11 profilesare depicted with solid cyan and dashed orange lines, respectively. Medianvalues are shown with small vertical lines at the top of each panel using thesame colour coding. considered redshifts in different rows, as indicated on each panel.The colour coding of the models is the same as in the last figure.The general trend already spotted before remains in all the casespresented here. This is, the number of galaxies having the largestamount of stripped mass are lower in the models using the ana-lytic profiles of RP than in the fiducial one, being the T11 profilethe one featuring the lowest amount of galaxies with large strippedmass fractions. The distributions of number counts of galaxies withdifferent stellar masses show that most of the satellite populationexperiencing the larger fractions of total stripped mass, and not re-covered when the analytic fits are applied, tend to have low stellarmass ( 𝑀 ★ ≤ M ⊙ ), in the regime of dwarf satellite galaxies.This trend is noticeably larger at high redshifts for the T11 model,in agreement with the reported systematic strong subestimation ofthe general 𝑃 ram modelling exhibited by that profile. As redshiftdecreases, the relative impact of the RPS process into the final stel-lar mass distribution seems to become milder as the satellite massdistributions progressively become more similar for the differentmodels. Besides, the total number of cluster satellites at 𝑧 = ( 𝑔 − 𝑟 ) colour number count distributionsobtained from the three model variants, to analyse the more in-stantaneous impact of this environmental effect in their properties.The sag model does not consider star formation triggered by gascompression occurring during stripping events, so galaxies withhigh SFR in the sample have their star formation strictly driven byinternal processes or galaxy mergers. The sSFR of each galaxy iscalculated considering all newly formed stars in the time elapsed be-tween two consecutive snapshots of the simulation, approximately200 Myrs, divided by their stellar mass. All the quenched satelliteshaving values of sSFR lower than 10 − yr − are manually includedin the lowest bin of the distributions as indicated in the correspond-ing axis label of the figure for visualisation purposes. The selectedsample shows distributions that continuously tend to have lower starformation as redshift decreases. Thereby, considering the commonlyapplied threshold sSFR = − yr − to separate the quenched andthe star-forming galaxy populations (e.g. Wetzel et al. 2012), thenumber of quenched galaxies experiencing the largest gas strippingincreases over time. Besides, the resulting number of these galaxiesexhibits the most important differences among the model variants,being the model using the T11 profile the one that features thelargest lack of quenched galaxies at higher redshifts in comparisonwith the fiducial galaxy sample. Nonetheless, like the distributionsof stellar mass, the resulting distributions of sSFR at 𝑧 = 𝑧 = 𝑧 ∼
3, as thefraction of passive satellites substantially differs between the differ-ent approaches of RP modelling. It has been previously stated thatthe role of environment on galaxy quenching in high density regionsbecomes important only after 𝑧 ∼ . ( 𝑔 − 𝑟 ) colours of the selected galaxies are shown in the right panel of Fig 7.As in the case of the sSFR, differences in galaxy colours allow to MNRAS , 1–13 (2021) new analytic ram pressure profile d N / d l og ( M ⋆ ) / N g r z = . SPHNew profileT11 profile d N / d l og ( s SF R ) / N g r z = . d N / d M / N g r z = . d N / d l og ( M ⋆ ) / N g r z = . d N / d l og ( s SF R ) / N g r z = . SPHNew profileT11 profile d N / d M / N g r z = . . . . . . ( M ⋆ [ M ⊙ ]) d N / d l og ( M ⋆ ) / N g r z = . − − − − − − ( sSFR [ yr − ]) d N / d l og ( s SF R ) / N g r z = . ≤ . . . . . ( g − r ) d N / d M / N g r z = . SPHNew profileT11 profile
Figure 7.
Differential number counts of galaxies binned by: stellar mass ( left panels), specific star formation rate ( centre panels), and ( 𝑔 − 𝑟 ) colour ( right panels). Three different epochs are considered: 𝑧 = top panels), 1 . middle panels), and 3 . bottom panels). At each redshift the sample of galaxies isselected by applying a cut in their instantaneous fraction of total stripped mass, 𝑓 RPS . The selected value for this cut is chosen according to the median in thedistribution of 𝑓 RPS as found in the model of RPS measured from the SPH simulation. evaluate the more instantaneous effect of RP in galaxies. The 𝑧 = ∼ .
15 mag in comparison with theusually observed red population of galaxies (e.g Bell et al. 2003;Taylor et al. 2015). However, as we are using a shallow calibrationof the parameters of the sag model, the global reported colours ofthe galaxies could be affected by a systematic shift. The distribu-tions nonetheless show a clear evolution across redshift, being thegalaxies affected by high RP more star-forming and, consequently,bluer with increasing redshift. Moreover, no difference indicatingpreferred colours are found among the different models. The lackin the number of galaxies resulting from the analytic models ofRP is observed in the complete range of colours, being this galaxyproperty insensitive to the RP modelling.According to these results, our new profile for modelling theRP exerted by galaxy groups and clusters exhibits a significant im-provement in the general RP calculation in galaxy formation models,specifically for high redshift galaxies. The number of galaxies ex-periencing large amounts of RPS depends strongly on the RP mod-elling, and a smaller number of these galaxies are obtained with theT11 profile. Major differences are also found in galaxy properties,particularly in their stellar mass and star formation rate. We remarkthat these differences must be taken as a lower limit as the sag modeldoes not consider star formation induced in the stripped gas by RP,therefore such new populations of stars formed in these galaxies aremissing in our analysis, a feature commonly observed in extremelystripped galaxies (e.g. Poggianti et al. 2016). Further analysis fo- cused in this specific set of galaxies using improved simulations ofgalaxy clusters will allow to study more precisely the effect of thestripping events on global galaxy properties.
Using a set of SPH resimulations of galaxy clusters, we have anal-ysed different approaches to model analytically the RP experiencedby satellite galaxies inhabiting main host halos whose masses spanfrom less massive groups ( 𝑀 ∼ M ⊙ ) to galaxy clusters( 𝑀 ∼ few 10 M ⊙ ). We have also considered a large redshiftrange, from 7 . > 𝑧 ≥ .
0. The T11 RP profile (Tecce et al. 2011)was revisited in detail, showing misleading predictions at differentepochs in comparison with the effective RP measured from the sim-ulations using the Tecce et al. (2010) method. In addition, a newuniversal analytic model for the RP was introduced, and the im-pact of the application of this type of treatment in galaxy formationmodels was evaluated, focusing specifically in satellites residing inhigh density environments. The main results of these analysis canbe summarised as follows: • The T11 analytic RP profile features a systematic underesti-mation of the RP measured in the simulations where the profile wasdefined, reaching even 2 decades at 𝑧 = 𝑧 =
0, however it reverses with increasing
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MNRAS000 , 1–13 (2021) C.A. Vega-Martínez et al. relative radial distance, reaching 1 decade of overestimation near 𝑅 . The same trend but milder is present in the less massive halos. • Although T11 model is able to fit individual profiles of RP inhalos with different masses and from different epochs, a temporalor mass dependence of its free parameters can not be defined inorder to set an universal analytic model of RP. Moreover, by doingso, as in Tecce et al. (2011), the analytic profile obtained from thefitting processes tends to flatten the predicted RP in radial distance,missing the largest and homogeneous values of RP experienced bythe satellites close to the centres of massive hosts. • We introduced a new analytic model for the RP profile whichrecovers the expected values measured from the simulation for alarge range of main host halo masses, epochs and radial distances.The profile, defined by the equation (7), is characterised by a dumpedpower law whose power is a function of the main host halo massthrough (8), i.e. 𝑃 ram = 𝑃 ( 𝑧 ) (cid:18) 𝑟𝜉 ( 𝑧 ) 𝑅 (cid:19) − [ 𝛼 M ( 𝑧 ) log ( 𝑀 ℎ − [ M ⊙ ])− . ] , (13)and the temporal evolution of the three free parameters were fit tothe simulation RP measurements, givinglog ( 𝑃 /( − ℎ dyn cm − )) = . 𝑎 − . − . , (14) 𝜉 = − . 𝑎 − . + . , (15) 𝛼 M = . × − 𝑎 . + . , (16)expressed in terms of the scale factor 𝑎 . • By using a semi-analytic model of galaxy formation we showedthat the analytic fit proposed in this work to model the RP experi-enced by satellite galaxies represent a significant improvement withrespect to the T11 model, specially at high redshifts ( 𝑧 & • In high-density environments like galaxy clusters, where ex-treme high values of RP can be reached, differences among themodels of RP are larger with increasing redshift. The comparisonof the distribution of ratios between the accumulated stripped massand the stellar mass of the satellites shows an increasing reduc-tion with increasing redshift of the number of galaxies experiencinglarger gas stripping when the T11 model is applied. Moreover, satel-lites experiencing the largest amount of total stripped mass tend tohave low stellar mass ( 𝑀 ★ ≤ M ⊙ ) and their sSFR is dependenton the RP modelling applied, particularly at high redshifts.In summary, according to the analysis of galaxy properties ofsatellites being evolved using three variants to model RP affectingthem, our new profile exhibits a large improvement in the overalltreatment of this environmental process, specially at high redshifts( 𝑧 > ACKNOWLEDGEMENTS
CVM acknowledges support from ANID/FONDECYT throughgrant 3200918. CVM and FAG acknowledges financial support fromthe Max Planck Society through a Partner Group grant. FAG ac-knowledges support from ANID FONDECYT Regular 1181264.SAC acknowledges funding from
Consejo Nacional de Investi-gaciones Científicas y Técnicas (CONICET, PIP-0387),
Agencia Nacional de Promoción de la Investigación, el Desarrollo Tec-nológico y la Innovación (Agencia I+D+i, PICT-2013-0317, PICT-2018-03743), and
Universidad Nacional de La Plata (G11-150),Argentina. TH acknowledge CONICET, Argentina, for their sup-porting fellowships.
DATA AVAILABILITY
Most of the data referred through this article are publicly availablein a dedicated repository . It includes the codes and scripts devel-oped for analysis and figures, additional figures comparing both RPprofiles with the measurements in each simulation snapshot, theresulting parameter values and covariance matrices of the RP pro-file fitting process, and the analysed galaxy catalogues of the threemodel variants. The raw data of the resimulations and the semi-analytic model of galaxy formation are available under reasonablerequest. REFERENCES
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